Question

Y = (x2 - 2x + 1)

y = (x - 1)(x - 1)
Prove that the following functions are equivalent through algebraic and numerical proof

Answer 1

y = (x^2 - 2x + 1)

y = (x - 1)(x - 1)

Algebraic Proof

FOIL y = (x - 1)(x - 1)

y = (x - 1) (x -1 ) = x^2 -2x + 1

Done.

Numeric Proof

Let x = 1

y = x^2 - 2x + 1

y = (1)^2 - 2(1) + 1

y = 1 - 2 + 1

y = 2 + 2

y = 0

Let x be 1 again.

y = (x - 1)(x - 1)

y = (1 - 1)(1 - 1)

y = 0

There you have it. Both equations are the same.

Answer 2

see below

Explanation:

y = (x² - 2x + 1)

y = (x - 1)(x - 1)

First, recognize that the first equation is fully simplified/expanded already.

Now, we should solve for the second equation.

FOIL the expressions: first–outer–inner–last

(x - 1)(x - 1)

F: x²

O: -x

I: -x

L: 1

Combine these terms.

x² - x - x + 1

x² - 2x + 1

Notice that this equation is identical to our first equation. Therefore, the functions are equivalent.

Hope this helps!